An important feature of network communication is data integrity. Under Ethernet, for example, this is accomplished using a 32-bit Cyclic Redundancy Check (CRC32) field that is added to each Ethernet MAC (Media Access Control) frame. The CRC provides full protection against many types of errors, including up to 3 bit errors in a normal-size MAC frame and bursts of consecutive errors up to 32 bits long. Other combinations of errors may pass the CRC32 check with a small probability (up to 2^-32 for random error distribution).
If multiple errors occur on an Ethernet link, the MAC frame could pass the CRC32 check; this event is called false packet acceptance, and ideally it should never occur. For example, the data for a MAC frame could be received with multiple errors that by random chance produce the same CRC32 value as a MAC frame with no errors. In practice, communication errors can't be totally prevented; the desire is that false packet acceptance would be so rare that the time until one is expected to happen (mean time to false packet acceptance, or MTTFPA) is larger than the age of the universe (AOU—about 13 Billion years).
Several physical layer (PHY) types for Ethernet over backplanes, Optics, and copper cables, at 10 Gb/s data rates and above are defined in various clauses of the IEEE 802.3 standard. The bit error ratio (BER) required for these PHYs is typically 1e−12. With this BER, if errors are uncorrelated to each other, the probability that enough errors occur to prevent CRC32 from detecting them is low enough to ensure MTTFPA>AOU. If errors occur at a much higher rate (BER>>1e−12), then MTTFPA may not be as large as desired. Assuming the errors typically generated by the physical layer receiver are independent, the probability of having more than 3 errors in a frame is governed by a BER^4 term, and is thus extremely small, guaranteeing the required MTTFPA. Accordingly, specifying very low BER can be seen as a solution to false packet acceptance.
One of the usual components in high-speed receivers is the decision feedback equalizer (DFE). A DFE is helpful in reducing the probability of individual errors, but can introduce error propagation: once a bit is incorrectly decoded (a bit error occurs), it is more likely that the next bit will also be incorrectly decoded (the error will propagate). The probability of error propagation depends on the noise statistics and the DFE configuration; it can range between 0 (in the no-DFE case) to 0.5 (very strong DFE case). Therefore, the probability of bursts of 4 or more errors may be considerably higher than BER^4.
As long as the bits received on the physical medium are mapped to contiguous bits in a frame (as done in 10GBASE-KR), the capability of the CRC to detect a single burst of any length guards against false packet acceptance. However, newer encoding schemes require striping data bits across several lanes, and un-striping the physical lane bits back at the receiver. As a result, physical lane bits are mapped to frame bits in a non-contiguous way, and a burst is converted into a series of non-adjacent errors, against which the CRC does not protect perfectly. Statistical calculations show that with bit-muxing, error bursts may degrade MTTFPA to intolerable periods (thousands of years) unless they have sufficiently low probability.